On 11/02/2012 20:51, KenR wrote:
> I need to generate more "Ramsey" Numbers to further verify that only
> prime numbers can meet the criteria. Ramsey numbers are those
> generated from a simple criteria that is easy to check. I imported a
> CSV list into my Mathematica version 8 to check all 30,759 numbers
> that my Excel macro selected and they all turned out to be prime. That
> is all that my program selected from all odd numbers from 3 to
> 1,048,655, as large as my Excel program could test. I would further
> test my program using my Mathematica software but I would like some
> help to write the most efficient program to do the job. Right now, I
> am trying to write a while loop inside a do loop but don't know how to
> exit the loop before the counter becomes 0 in the case that it is
> clear that P is not prime.
>
> The check is to do the following binary recursive sequence mod P and
> check to see that the (P-1)/2 term is zero and no term prior to that
> is zero. If so then I believe P should be prime based upon the results
> so far.
>
> The test sequence is S(0) = 2, S(1) = 3, S(n) = 6*S(n-1) - S(n-2) - 6.
> It appears that S((P-1)/2) is divisible by P then P is very likely
> Prime, but I am interested in a test that is valid only for primes.
> S((35-1)/2) is divisible by 35 but that is not the first term
> divisible by 35. Only about 1/3 of the primes seem to meet the more
> restricted criteria, i.e. the sequence has no term divisible by P
> prior to S((P-1)/2).
>
>
Using Do and While loops, tends to be frowned upon by some purists, but
I think they are a good way to take a first stab at many problems.
To exit a Do or While loop on some condition, use
If[condition,Break[]];
If you want to exit multiple layers of loops, and/or function calls, use
Catch/Throw. These are inefficient if used, but if you are going to
execute them at most once, there is no problem.
David Bailey
http://www.dbaileyconsultancy.co.uk